Kindly help with the following question:

Box A and Box B contain 109 apples and oranges. 6/11 of Box A are apples and 4/9 of Box B are oranges. What is the total number of apples in both boxes?

Solution:

From the data given in the question and since number of fruits in Box A and B can only be whole numbers, we can use the Common Multiple method here. Based on the respective fractions of apples and oranges in Box A and B, the total number of fruits in box A must be a multiple of 11 and box B must be a mulitple of 9.

List out the multiples of both 11 and 9 to find a pair of multiples that will add up to 109.

A: 11, 22, 33, 44, 55, 66, 77, 88, 99

B: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

The underlined numbers 55, 54 add up to 109. Therefore, total number of fruits in Box A = 55; total number of fruits in Box B = 54.

Number of apples in Box A = (6 / 11) x 55 = 30

Number of apples in Box B = (5 / 9) x 54 = 30

Therefore, total number of apples in both boxes is 60.

Are there any other method apart from this?

Thank you in advance for your assistance.